Traffic modeling plays a fundamental role in traffic engineering of telecommunications networks, whether they be circuit switched or packet switched, voice or data. In the Public Switched Telephone Network (PSTN), Erlang models have been widely used for trunk engineering and sizing. Application of traffic models to packet-switched environments, including broadband packet-switched environments, has been more difficult and, thus, remains an active area of research.
Packet-switched networks include terminals connected via access lines to a packet switched infrastructure comprised of network elements or nodes connected to one another. Network elements (e.g., routers, switches, multiplexers, etc.), located at various points in a network, may provide switched or routed connections between terminals. Messages may be transferred between terminals as sequences of packets. Native link layer protocols, such as Asynchronous Transfer Mode (ATM), Frame Relay, and Ethernet, and network layer protocols, such as Internet Protocol (IP) traversing broadband link layer subnets, may be used to format and decode packets. Upon receiving a packet, a network element may determine the next node in the transmission path and then place the packet in a queue for transmission.
The arrival of packets at a given network element may be a random process. Accurate traffic models of the arrival process assist network engineers in making effective capacity decisions regarding bandwidth and buffer resources in network elements. Thus, accurate traffic models allow efficient use of bandwidth and buffer resources and minimize network costs.
A switched Poisson process (SPP) is a traffic model that may be used to represent a packet arrival process. An SPP is a special case of a Markov-modulated Poisson process (MMPP). An MMPP is a time-varying Poisson process that “modulates” among different phases. In general, an N-phase MMPP has Poisson-distributed packet arrivals with arrival rate λj, when the MMPP is in phase j, where 1≦j≦N. For example, a three-phase MMPP is Poisson with an arrival rate modulating among λ1, λ2, and λ3 during phases one, two, and three, respectively. Rates of transition between different phases are governed by a Markov chain. An SPP is a two-phase MMPP and, therefore, alternates between two rates, λ1 and λ2, in accordance with transition rates, q1 and q2, from phase one to two, and two to one, respectively.
It would therefore be desirable to provide a network element capable of accurately modeling a packet arrival process and, in particular, capable of estimating parameters λ1, λ2, q1, and q2 of an SPP traffic model.